Solve - 4x^35> 2 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x < - \frac{3 100}{10}

Alternative Form

x \in (- \infty, - \frac{3 100}{10})

Evaluate

- 4 x^{3} \times 5 > 2

Multiply the terms

- 20 x^{3} > 2

Move the expression to the left side

- 20 x^{3} - 2 > 0

Rewrite the expression

- 20 x^{3} - 2 = 0

Move the constant to the right-hand side and change its sign

- 20 x^{3} = 0 + 2

Removing 0 doesn't change the value,so remove it from the expression

- 20 x^{3} = 2

Change the signs on both sides of the equation

20 x^{3} = - 2

Divide both sides

\frac{20 x ^{3}}{20} = \frac{- 2}{20}

Divide the numbers

x^{3} = \frac{- 2}{20}

Divide the numbers

More Steps

x^{3} = - \frac{1}{10}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 - \frac{1}{10}

Calculate

x = 3 - \frac{1}{10}

Simplify the root

More Steps

x = - \frac{3 100}{10}

Determine the test intervals using the critical values

x < - \frac{3 100}{10} x > - \frac{3 100}{10}

Choose a value form each interval

x_{1} = - 1 x_{2} = 1

To determine if x < - \frac{3 100}{10} is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < - \frac{3 100}{10} is the solution x_{2} = 1

To determine if x > - \frac{3 100}{10} is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < - \frac{3 100}{10} is the solution x > - \frac{3 100}{10} is not a solution

Solution

x < - \frac{3 100}{10}

Alternative Form

x \in (- \infty, - \frac{3 100}{10})

Show Solution